(S|D|C|Z)GESVD¶

Single, double, single complex, and double complex GESVD.

Description¶

Computes the singular value decomposition (SVD) of a general matrix, and optionally the right/left singular vectors.

The matrix A is decomposed:

$A = U \mult \Sigma \mult \herm{V}$

The matrix $\Sigma$ is an MxN matrix that is zero except on the diagonal. U is an MxM unitary matrix, and V is an NxN unitary matrix. The diagonal elements of $\Sigma$ are the singular values, ordered from largest to smallest in magnitude.

LAPACK Interface¶

void sgesvd(const char *JOBU, const char *JOBVT, const qml_long *M,
    const qml_long *N, float *A, const qml_long *LDA, float *S, float *U,
    const qml_long *LDU, float *VT, const qml_long *LDVT, float *WORK,
    const qml_long *LWORK, qml_long *INFO);

void dgesvd(const char *JOBU, const char *JOBVT, const qml_long *M,
    const qml_long *N, double *A, const qml_long *LDA, double *S,
    double *U, const qml_long *LDU, double *VT, const qml_long *LDVT,
    double *WORK, const qml_long *LWORK, qml_long *INFO);

void cgesvd(const char *JOBU, const char *JOBVT, const qml_long *M,
    const qml_long *N, qml_single_complex *A, const qml_long *LDA,
    float *S, qml_single_complex *U, const qml_long *LDU,
    qml_single_complex *VT, const qml_long *LDVT,
    qml_single_complex *WORK, const qml_long *LWORK, float *RWORK,
    qml_long *INFO);

void zgesvd(const char *JOBU, const char *JOBVT, const qml_long *M,
    const qml_long *N, qml_double_complex *A, const qml_long *LDA,
    double *S, qml_double_complex *U, const qml_long *LDU,
    qml_double_complex *VT, const qml_long *LDVT,
    qml_double_complex *WORK, const qml_long *LWORK, double *RWORK,
    qml_long *INFO);

Arguments¶

JOBU	What to compute for U, ‘A’ (all), ‘S’ (left singular vectors), ‘O’ (overwrite A), ‘N’ (none)
JOBVT	What to compute for VT, ‘A’ (all), ‘S’ (right singular vectors), ‘O’ (overwrite A), ‘N’ (none)
M	Number of rows of A
N	Number of columns of A
A	Matrix of size M x N, overwritten on exit
LDA	Leading dimension of A
S	Array of size min(M, N), singular values in decreasing order
U	Matrix containing left singular vectors as columns
LDU	Leading dimension of U
VT	Matrix containing right singular vectors as rows
LDVT	Leading dimension of VT
WORK	Workspace of size at least LWORK
LWORK	Size of workspace (-1 to query)
RWORK	Workspace of size 5*min(M, N)
INFO	0 on success, <0 for bad arguments, >0 if no convergence